Modeling the obliquity of Mercury

Mercury is the target of the space missions MESSENGER and BepiColombo, that will in particular observe its rotation to get information on its internal structure. This requires a rigorous modelization of this rotation. A difficulty comes from the obliquity of Mercury, that behaves adiabatically, and so is tough to simulate over a short timescale without generating free oscillations. These free oscillations are due to the inaccuracy of the initial conditions, that are difficult to determine because they correspond to an equilibrium of the complete, perturbed problem. We here propose formulae linking the long-term behavior of the obliquity of Mercury with its gravity parameters C , C and C/( ), based on Peales (1981) formula. We use for that a fitted precessional motion of Mercury that we include in averaged rotational equations, and we show that the solutions extracted can be used in a realistic simulation suitable to a space mission. We estimate that these solutions induce an error lower than 3% in the modelization of Mercurys obliquity. Thus, an inversion of the observed orientation of Mercury could lead to an uncertainty of 3% on Mercurys inertial polar momentum, if we neglect the other sources of error.